results of the parameter studies and prioritization for ... scp0-ga-2010-265754 rivas_bam_...

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RIVAS

Railway Induced Vibration Abatement Solutions

Collaborative project

Results of the parameter studies and prioritization for prototype

construction for slab track

Deliverable D3.3

Submission date: 17/05/2012

Project Coordinator:

Bernd Asmussen

International Union of Railways (UIC)

[email protected]

mailto:[email protected]

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Title Results of the parameter studies and prioritization for prototype construction for slab track

Domain WP 3, Task 3.4

Date 15/05/2012

Author/Authors Lutz Auersch (BAM)

Partner ALSTOM, BAM, DB, D2S, ER, RailOne

Document Code RIVAS_BAM_ WP3_D3_3_V04

Version 03

Status Final

Dissemination level:

Project co-funded by the European Commission within the Seventh Framework Programme

Dissemination Level

PU Public X

PP Restricted to other programme participants (including the Commission Services)

RE Restricted to a group specified by the consortium (including the Commission) Services)

CO Confidential, only for members of the consortium (including the Commission Services)

Document history

Revision Date Description

1 30/03/2012 First Draft

2 30/04/2012 Second Draft

3 07/05/2012 Third Draft

4 15/05/2012 Final

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1. EXECUTIVE SUMMARY

Slab tracks with wide sleepers on under sleeper pads have been investigated in a parameter

study using a finite-element boundary-element method. The slab track is modelled in detail

by the finite element method. The infinite soil is modelled by the boundary element method

as a homogeneous half-space. The track-soil system is coupled with a rigid wheelset mass

so that the vehicle-track interaction is included. Transfer functions are calculated in

frequency domain without and with vehicle-track interaction, the compliance of the track and

the mobilities of the soil at different distances from the track. Finally, the ratios between the

ground vibration amplitudes with and without mitigation measure are calculated to quantify

the effectiveness of the mitigation measure.

A slab track with an under sleeper pad of a stiffness of kS = 50 106 N/m, which can also be

expressed as a stiffness per area of kS’’ = 3.6 107 N/m3 = 0.036 N/mm3, yields a vehicle-track

resonance frequency of 32 Hz. Whereas the vibration at this frequency are amplified, higher

frequencies are reduced. The insertion loss of this solution is up to 25 dB at 80 Hz for the

ground vibrations in comparison to the reference slab track system (GETRAC system without

sleeper pads but with soft rail pads).

The stiffness of the under sleeper pad has a strong influence on the vibration reduction. The

softest sleeper pad yields the lowest vehicle-track resonance frequency and the best

reduction of the ground vibration. The influence of other parameters has been examined,

such as the stiffness of the rail pads, the stiffness of the slab material, the stiffness of the

sleeper material, and the distance between the sleepers. All these parameters show no or

only a minor influence on the mitigation effect.

As a conclusion, a wide sleeper slab track with under sleeper pads is recommended for

further testing with under sleeper pads as soft as possible and with the highest possible

sleeper mass. The stiffness of the rail pads can be chosen according to acoustical

requirements.

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2. TABLE OF CONTENTS

1. Executive summary ........................................................................................................ 3

2. Table of contents ............................................................................................................ 4

3. Introduction .................................................................................................................... 6

4. Methods of vehicle-track-soil interaction ......................................................................... 8

4.1 Finite-element boundary-element method ............................................................... 8

4.2 Vehicle-track interaction .......................................................................................... 8

4.3 Validation of the methods ........................................................................................ 9

5. Parameter study ............................................................................................................10

5.1 Model of the track and the vehicle ..........................................................................10

5.2 Parameters of the track ..........................................................................................10

5.3 Output quantities ....................................................................................................12

6. Results for the reference track.......................................................................................13

7. Results for slab tracks with wide sleepers on sleeper pads ...........................................14

8. Complementary results .................................................................................................15

8.1 Variation of the rail pad stiffness.............................................................................15

8.2 Variation of the slab stiffness ..................................................................................15

8.3 Variation of the sleeper stiffness.............................................................................15

8.4 Variation of the sleeper distance ............................................................................16

9. Conclusion ....................................................................................................................17

10. References ................................................................................................................18

11. Appendix A – The track model ...................................................................................20

12. Appendix B – Results of the reference slab track .......................................................23

13. Appendix C – Results of the slab track with different under sleeper pads ..................26

14. Appendix D – Insertion loss compared to the reference ballast track .........................32

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15. Appendix E – Complementary results of slab tracks with sleeper pads of 50 kN/mm .37

16. Appendix F – The GETRAC system without and with under sleeper pads .................50

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3. INTRODUCTION

Train-induced vibrations are becoming a growing problem all over Europe. The European

research project “Railway induced vibration abatement solutions (RIVAS)” is focussed on

measures to be applied at the source, at the track, in the transmission and propagation path

and at the vehicles. The work package 3 “Mitigation measures track” includes the task 3.4

which is concerned with “Mitigation measures for slab track” [9]. A combined finite-element

boundary-element model is used to investigate the vibration reduction potential of different

solutions. The influence of the following components, sleeper pads, rail pads, sleeper and

slab stiffness, and the sleeper distance is analysed.

The comparison of different slab track systems will be given in Deliverable 3.11 whereas the

present report concentrates on a particular slab track, the GETRAC system with under

sleeper pads (Figure 16-1). The GETRAC system is characterised as a pre-stressed mono-

block sleeper equipped with an under sleeper pad and laid on a stiff asphalt slab. The wide

sleepers of this slab track system provide a higher elastically supported mass than other slab

track systems (e.g. Sonneville LVT). The higher sleeper mass has been identified as

beneficial for the vibration abatement in Deliverable 3.2.

Tracks with under sleeper pads have been investigated in a wide parameter study in

Deliverable 3.2 for ballasted tracks [8]. It has been found that the parameters with the

strongest influence on the reduction of ground vibration

the stiffness of the under sleeper pad,

the mass of the sleeper,

and the width of the sleeper.

Other parameters, such as

the stiffness of the rail pads,

the bending stiffness of the track,

the stiffness of the ballast,

the sub-soil, the soil, and the layering of the soil

showed no or only a minor influence on the mitigation effect. Most of these results can also

be used for the slab track considered in this report. These parameter variations are not

repeated here, but some more parameters such as

the stiffness of the rail sleeper pad,

the stiffness of the sleeper,

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the stiffness of the slab,

and the distance between the sleepers

are checked for their influence on the mitigation of ground vibrations.

The structure of the report is as follows. The summary, table of content and introduction are

numbered as sections 1, 2, and 3. Section 4 describes the methods of calculation using the

available references, the finite element method for the track, the boundary element method

for the infinitely extended soil, and the interaction with a rigid body model of the vehicle.

Section 5 gives an overview on the parametric study. Section 6 presents the results for the

reference track, Section 7 the results for the isolated slab tracks on different sleeper pads,

and Section 8 the results of the parameter variations. The effectiveness of the mitigation

measures is evaluated by the ratio of the ground vibrations for the isolated slab track and the

reference track. Section 9 presents the conclusions.

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4. METHODS OF VEHICLE-TRACK-SOIL

INTERACTION

4.1 FINITE-ELEMENT BOUNDARY-ELEMENT METHOD

The track-soil systems are modelled by the combined finite-element boundary-element

method [1, 5, 7]. The track including the rails, rail pads, sleepers, under sleeper pads, and

the slab is modelled by the finite element method whereas the infinitely extended soil is

modelled by the boundary element method. The dynamic stiffness matrix of the soil is

established by using the Green’s functions of an elastic layered half-space [3, 7]. All

calculations (Green’s functions, boundary matrix and finite element matrices) are performed

in frequency domain. Special additional methods (within the FEBEM) have been developed

for infinite tracks [6] which are also applied to this study.

The results of a FEBEM calculation are the frequency-dependent compliance uR/FT of the

track (rail displacements uR divided by the dynamic harmonic wheelset load FT on the track)

and mobility vi/FT of the soil (ground particle velocity divided by the dynamic harmonic

wheelset load FT on the track).

4.2 VEHICLE-TRACK INTERACTION

The influence of the vehicle on the ground vibration can be calculated in a second step in

frequency domain as well [4]. The compliance of the track is inverted to the track stiffness

KT = (uR/FT’)-1. A corresponding dynamic stiffness KV of the vehicle can be calculated by

multi-body dynamics [2]. It can be approximated by the inertia of the wheelset KV = -mW2 in

the frequency range of interest. The vehicle is excited by the irregularities s of the track

(alignment and rail roughness) and the vehicle (out-of-roundness and roughness of the

wheel).

The transfer function between the irregularities s and the force FT on the track can be

calulated as

VT

VTT

KK

KK

s

F

The vehicle-track interaction can also be expressed as

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VT

T

V

T

KK

K

F

F

if the force FV = -KVs is used which is generated by the vehicle and the irregularities in case

of a rigid track.

After the vehicle-track interaction is solved, the ground vibration can be calculated by

multiplying the vehicle-track transfer function and the mobilities of the soil

VT

T

T

i

V

T

T

i

V

i

KK

K

F

v

F

F

F

v

F

v

.

At the end, two different tracks (isolated and un-isolated track) are compared by comparing

the vibration at the same soil point xi. The velocity ratio vi,U /vi,I of the un-isolated and isolated

track can be built by the transfer functions without specifying the excitation

IVT

T

T

i

UVT

T

T

i

V

Ii

V

Ui

Ii

Ui

KK

K

F

v

KK

K

F

v

F

v

F

v

v

v

,

,

,

,

,

,

.

4.3 VALIDATION OF THE METHODS

The present methods of track dynamics and vehicle-track interaction have been used since

1982 [10] for many reports and publications. They have been verified by comparison with

other methods [11] and with several measurements [2, 4, 5, 10].

The methods are used for a single fixed axle load, not for moving train sets. This is sufficient

to determine the frequency-dependent efficiency of the mitigation measures to reduce the

ground response to dynamic loads. Effects on the excitation of the ground vibration such as

reduced track errors and a reduced stiffness variation (parametrical excitation) are not

discussed here, see [2, 4] for corresponding methods and results. Additional software tools

have been developed by BAM for the prediction of railway induced vibration.

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5. PARAMETER STUDY

5.1 MODEL OF THE TRACK AND THE VEHICLE

Figure 11-1 to Figure 11-3 show the finite element model of the track which has a length of

6.68 m. It consists of two rails, eleven sleepers with rail pads and under sleeper pads, a slab,

and the infinite soil. End elements at the rails approximate the behaviour of an infinite track.

The track is excited by a dynamic harmonic axle load (a pair of vertical forces) which acts on

the rails above the central sleeper.

The only vehicle parameter is

the wheelset mass mW = 1500 kg

5.2 PARAMETERS OF THE TRACK

A slab track with wide sleepers on under sleeper pads with the following parameters is

analysed:

bending stiffness of the rails (UIC60) EI = 2 x 2.1 1011 x 3.0 10-5 Nm2 = 12.6 106 Nm2,

mass per length of the rails m’R = 2 x 60 kg/m,

distance of the rail pads d = 0.6 m

stiffness of the rail pads kR = 300 106 N/m,

modulus of elasticity of the sleepers ES = 3 1010 N/m2,

mass density of the sleepers S = 2.5 103 kg/m3,

length of the sleepers aS = 2.6 m,

height of the sleepers hS = 0.2 m,

width of the sleepers bS = 0.52 m ,

stiffness of the sleeper pads kS = 50 106 N/m,

width of the slab aB1 = 3.2 m,

height of the slab hB = 0.3 m,

elasticity modulus of the slab EP = 4 109 N/m2,

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shear modulus of the soil G = 8 107 N/m2,

shear wave velocity of the soil vS = 200 m/s

mass density of the soil = 2 103 kg/m3,

Poisson’s ratio of the soil = 0.33,

hysteretic damping of the soil D = 2.5 %,

hysteretic damping of the elastic elements DP = DS = 10 %.

The following parameter variations are performed in this deliverable:

stiffness of the sleeper pads kS = 25, 50, 100, 200 106 N/m,

stiffness of the rail pads kR = 300, 1000 106 N/m,

elasticity modulus of the slab EP = 0.48, 1, 4, 10, 30 109 N/m2,

modulus of elasticity of the sleepers ES = 1.5, 3, 6 1010 N/m2,

distance of the rail pads d = 0.6, 0.65 m.

More parameter variations, for example variations of the sub-soil, the soil, and the layering of

the soil have been analysed in Deliverable 3.2 for ballasted tracks. The minor influence on

the reduction of ground vibration could also apply for isolated slab tracks.

The stiffness of the under sleeper pads

kS = 25, 50, 100, 200 106 N/m

can also be expressed as a stiffness per area

k’’S = 18, 36, 72, 144 106 N/m3 or

k’’S = 0.018, 0.036, 0.072, 0.144 N/mm3 (according to DIN 45673).

For real under sleeper pads, it must be observed that they have different stiffnesses for the

high static load and the small additional dynamic loads. The dynamic stiffness values must

be applied for the reduction of the ground vibration due to dynamic loads.

A slab track without sleeper pads is calculated as a reference slab track. The reference slab

track has the same parameters as given before but it has no under sleeper pads. The

stiffness of the rail pads is taken as

kR = 40 106 N/m,

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so that the reference slab track has a realistic compliance. (In addition, the reference ballast

track of Deliverable 3.2 is used in Appendix D to facilitate more comparisons.)

5.3 OUTPUT QUANTITIES

The following quantities are presented as the results of the track-soil and the vehicle-track

interaction:

The compliance uR/FT or uR/FV of the track, without and with vehicle-track interaction,

the mobility vi/FT or vi/FV of the soil at 4, 8, 16, and 32 m from the centre of the track, without

and with vehicle-track interaction,

and the ground vibration ratios vi,U /vi,I (insertion loss of the slab track with under sleeper pad)

at 4, 8, 16, and 32 m from the centre of the track.

All ground vibration ratios vi,U /vi,I and all ground vibrations (mobilities vi/F) in Appendix C and

E are calculated with vehicle-track interaction.

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6. RESULTS FOR THE REFERENCE TRACK

At first, the results of the FEBEM calculation without any vehicle-track interaction are shown

in Figure 12-1a. The track compliance is almost constant at uR/FT = 6 10-9 m/N for all

frequencies. That means a rail displacement of 0.6 mm under a 100 kN axle load. At

frequencies higher than 100 Hz, a weak increase of the compliance is observed. The

mobilities of the soil (Figure 12-2a) show some characteristic changes in the frequency range

of interest. At first, the soil mobilities increase with frequency up to 40 Hz. At higher

frequencies, the mobilities turn to be constant or decreasing which is due to the material

damping of the soil, which has its strongest effect on the far-field points of the soil, and due

to the distribution of the excitation force across the track.

The compliance of the track and the dynamic stiffness of the vehicle (wheelset) yield the

vehicle-track transfer function. The compliance of the track is multiplied by this vehicle track

transfer function in Figure 12-1b, and including the vehicle track interaction yields

considerably different results. Due to the soft rail pads of the reference track, a clear vehicle-

track resonance can be observed at 50 Hz and a strong reduction of rail displacements at

higher frequencies. The soil mobilities are multiplied by the vehicle-track transfer function in

Figure 12-2b, and the soil mobilities at 4, 8, 16, and 32 m show the same vehicle-track

resonance at 50 Hz and the strong decrease at higher frequencies as the rail compliance

with vehicle-track interaction.

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7. RESULTS FOR SLAB TRACKS WITH WIDE

SLEEPERS ON SLEEPER PADS

The most important parameter to reduce the train induced ground vibration by under sleeper

pads is the stiffness of the pads. The stiffness of the under sleeper pads is varied as kS = 25,

50, 100, 200 106 N/m. Stiffer under sleeper pads are possible, but they have almost no

positive effect below 100 Hz.

The softest under sleeper pad yields a track compliance higher than 0.01 mm/kN (1 mm per

100 kN axle load, Figure 13-1a). Stiffer under sleeper pads are below this value. All

investigated under sleeper pads have track-pad resonances below 160 Hz, starting at 25 Hz

for the softest and ending at 80 Hz for the stiffest sleeper pad. Including the wheelset mass

yields a somewhat lower vehicle-track resonance frequency between 22 and 50 Hz (Figure

13-1b). The same lower resonance frequencies are found for the ground vibrations at the

different distances (Figure 13-2 and Figure 13-3). The resonance amplification has lower

values in case of stiffer sleeper pads. After the resonance, a strong decrease of the transfer

functions is observed. The softest under sleeper pads yield the strongest reduction. The

reduction is quantified by the ratio of the ground vibration of the reference track to the ground

vibration of the slab track with sleeper pads (Figure 13-4 and Figure 13-5). These ratios

(insertion losses) start at the value 1 (0 dB) at low frequencies. They decrease until the

vehicle-track resonance of the isolated track is reached at 25 to 40 Hz. A strong increase

follows up to 64 or 80 Hz where the maximum value of the insertion loss is found. At higher

frequencies, the insertion loss varies around lower values. For the stiffness kS = 50 106 N/m

of the sleeper pad, the highest insertion loss is around 20 dB at 64 or 80 Hz. The maximum

insertion loss is higher for the softest pad stiffness (20 to 30 dB) and lower for the stiffer

sleeper pads. It is also higher for the far-field points where the sleeper pad of

kS = 50 106 N/m yields an insertion loss of 25 dB. The high insertion loss values are due to

the resonance of the reference slab track and changes of the load distribution which have

different effects at different distances from the track. Therefore, the insertion loss should be

assured by using different observation points (Figure 13-4 and Figure 13-5) and different

reference tracks (see Appendix D). The minimum of the insertion loss due to the vehicle-

track resonance of the isolated track is smallest for the softest sleeper pad reaching a value

of -10 dB.

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8. COMPLEMENTARY RESULTS

The analyses in the following Sections have been done to check if the effectiveness of the

under sleeper pads is influenced by certain parameters. The stiffness of the under sleeper

pad is kept constant at kS = 50 106 N/m.

8.1 VARIATION OF THE RAIL PAD STIFFNESS

In deliverable 3.2 of RIVAS [8], it has been found that a soft rail pad could give a worse

efficiency of soft sleeper pads. Therefore, the isolated slab track is also calculated with a

stiffer rail pad of kR = 1000 kN/mm to check whether the rail pad of kR = 300 kN/mm is

already stiff enough to achieve the optimum effect of the under sleeper pad. As a result, the

static displacement is reduced by 1 % if the stiff rail pads are used (Figure 15-1). Some small

differences can be found at high frequencies for the track compliance as well as for the soil

mobilities in Figure 15-2 and Figure 15-3, but there is no clear tendency that the stiffer rail

pads can improve the mitigation.

8.2 VARIATION OF THE SLAB STIFFNESS

The slab material has been varied in a wide range. The elasticity modulus of three different

asphalt materials has been chosen, and in addition a higher elasticity modulus (the elasticity

modulus of concrete) and a lower elasticity modulus (comparable to the elasticity modulus of

a stiff ballast) are taken in to account. The compliances of the tracks with different slab

materials are identical (Figure 15-4). The differences are found for the ground vibration at

high frequencies above 50 Hz (Figure 15-5 and Figure 15-6). The differences are usually in

the order of the different elastic moduli, but the stiffest slab material yields at some

frequencies the highest and at some frequencies the lowest value. A general tendency, that

a stiffer slab material can improve the mitigation effect of the under sleeper pads, must be

denied. A similar minor influence on the track and ground vibration might be expected for the

slab mass.

8.3 VARIATION OF THE SLEEPER STIFFNESS

The elasticity modulus of concrete varies in certain limits. In the present report a wider range

of stiffness values, 1.5 to 6 1010 N/m2, has been examined to find clearer effects. Some small

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differences have been found in Figure 15-7 to Figure 15-9 for frequencies above 80 Hz. At

80 Hz, the stiffest material yields the highest amplitudes whereas at 160 Hz, the softest

material has the highest amplitudes of the three materials. There is no clear order of

amplitudes, and the differences vary with frequency. So it is concluded that there is an

influence of the sleeper stiffness but without a clear advantage for the stiffer or softer

material.

8.4 VARIATION OF THE SLEEPER DISTANCE

On Figure 15-10 to Figure 15-12 two sleeper distances are compared, d = 0.6 m and 0.65 m.

The displacements above the sleeper differ by 4 %. The ground vibration curves are almost

identical. So it is concluded that the small variation of the sleeper distance of less than 10 %

yields only negligible changes in the behaviour and effectiveness of the under sleeper pads.

The distance between the sleepers has an influence on the parametric excitation which has

not been studied here.

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9. CONCLUSION

Slab tracks with wide sleepers on under sleeper pads have been investigated in a parameter

study using a finite-element boundary-element method. The influence of different parameters

on the reduction of the ground vibration has been investigated.

The stiffness of the under sleeper pad has a strong influence on the vibration

reduction. The softest sleeper pad yields the lowest vehicle-track resonance

frequency and the best reduction of the ground vibration. For example, the sleeper

pad stiffness of kS = 50 106 N/m yields a vehicle-track resonance frequency of 32 Hz

and a maximum insertion loss of 25 dB at 80 Hz.

The influence of other parameters has been examined, such as

the stiffness of the rail pads,

the stiffness of the slab material,

the stiffness of the sleeper material,

and the distance between the sleepers.

All these parameters show no or only a minor influence on the mitigation effect.

These results are complementary to the results in Deliverable 3.2 for ballasted tracks on

sleeper pads where

the mass of the sleeper,

and the width of the sleeper

showed a positive effect on the vibration reduction, and

the stiffness of the sub-soil,

the stiffness and the layering of the soil

showed no or only a minor influence on the mitigation effect.

As a conclusion, a wide sleeper slab track with under sleeper pads is recommended for

further testing with under sleeper pads as soft as possible and with the highest possible

sleeper mass. The stiffness of the rail pads can be chosen according to acoustical

requirements.

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10. REFERENCES

[1] L. Auersch, G. Schmid: A simple boundary element formulation and its application to

wavefield excited soil-structure interaction. Earthquake Engineering and Structural

Dynamics 19, 1990, 931-947.

[2] L. Auersch: Zur Parametererregung des Rad-Schiene-Systems: Berechnung der

Fahrzeug-Fahrweg-Untergrund-Dynamik und experimentelle Verifikation am

Hochgeschwindigkeitszug Intercity Experimental. Ingenieur-Archiv 60, 1990, 141-156.

[3] L. Auersch: Wave propagation in layered soil: theoretical solution in wavenumber

domain and experimental results of hammer and railway traffic excitation. Journal of

Sound and Vibration 173, 1994, 233-264.

[4] L. Auersch: The excitation of ground vibration by rail traffic: Theory of vehicle-track-

soil interaction and measurements on high-speed lines. Journal of Sound and

Vibration 284, 2005, 103-132.

[5] L. Auersch: Dynamics of the railway track and the underlying soil: the boundary-

element solution, theoretical results and their experimental verification. Vehicle

System Dynamics 43, 2005, 671-695.

[6] L. Auersch: Dynamic axle loads on tracks with and without ballast mats – numerical

results of three-dimensional vehicle-track-soil models. Journal of Rail and Rapid

Transit 220, 2006, 169-183.

[7] L. Auersch: Wave propagation in the elastic half-space due to an interior load and its

application to ground vibration problems and buildings on pile foundations. Soil

Dynamics and Earthquake Engineering 30, 2010, 925–936.

[8] L. Auersch: Mitigation measures for ballasted tracks – sleeper, sleeper pads and

substructure – results from the finite-element boundary-element method. Appendix B

in B. Faure, E. Bongini, BAM, KUL: Results of the parameter studies and prioritization

for prototype construction for ballasted track. Deliverable 3.2 of RIVAS, 2012.

[9] „Railway Induced Vibration Abatement Solutions“, Description of Work. Collaborative

project for theme SST.2010.1.1-3. “Attenuation of ground-borne vibration affecting

residents near railway lines” in the seventh framework programme.

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[10] W. Rücker: Dynamic interaction of a railroad-bed with the subsoil. Proc. Conf. Soil

Dynamics and Earthquake Engineering. Southampton 1982, 435-448.

[11] W. Rücker, L. Auersch, M. Baeßler, K. Knothe, K. Popp, S. Savidis, G. Schmid: A

Comparative Study of Results from Numerical Track-Subsoil Calculations. In: K.

Popp, W. Schiehlen (eds.); Lecture Notes in Applied Mechanics “System Dynamics

and Long-Term Behaviour of Railway Vehicles, Track and Subgrade”, Berlin:

Springer-Verlag, 2003, 471-488.

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11. APPENDIX A – THE TRACK MODEL

Figure 11-1: Finite-element-model of the slab track

Rail Rail pad Sleeper Sleeper pad Slab

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Figure 11-2: Finite-element-model of the slab track, top view

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Figure 11-3: Finite-element-model of the slab track, view along and across the track

Rail Rail pad Sleeper Sleeper pad Slab

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12. APPENDIX B – RESULTS OF THE REFERENCE

SLAB TRACK

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Figure 12-1: Reference track, compliance of the track a) without and b) with vehicle-track

interaction

b)

a)

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Figure 12-2: Reference track, mobilities of the soil at 4, 8, 16, 32 m, a) without and

b) with vehicle-track interaction

b)

a)

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13. APPENDIX C – RESULTS OF THE SLAB TRACK

WITH DIFFERENT UNDER SLEEPER PADS

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Figure 13-1: Slab tracks on different under sleeper pads, kS = 25, 50, 100, 200 kN/mm,

compliances of the track a) without and b) with vehicle-track interaction

b)

a)

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mobilities of the soil at a) 4, b) 8 m distance from the track, including vehicle-track interaction

b)

a)

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mobilities of the soil at a) 16, and b) 32 m distance from the track, including vehicle-track

interaction

b)

a)

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insertion loss (reference slab track divided by isolated slab track) of the ground vibration at

a) 4, b) 8 m distance from the track

b)

a)

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insertion loss (reference slab track divided by isolated slab track) of the ground vibration at

a) 16, and b) 32 m distance from the track

b)

a)

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14. APPENDIX D – INSERTION LOSS COMPARED TO

THE REFERENCE BALLAST TRACK

The results for the slab track are additionally compared to the ballasted reference track which

is defined in the deliverable 3.2 “Mitigation for ballasted tracks” [8].

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insertion loss (reference ballast track divided by isolated slab track) of the ground vibration at


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Figure 14-3: Reference slab track, insertion loss (reference ballast track divided by reference

slab track) of the ground vibration at a) 4, b) 8 m distance from the track

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Figure 14-4: Reference slab track, insertion loss (reference ballast track divided by reference

slab track) of the ground vibration at a) 16, b) 32 m distance from the track

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15. APPENDIX E – COMPLEMENTARY RESULTS OF

SLAB TRACKS WITH

SLEEPER PADS OF 50 KN/MM

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Figure 15-1: Tracks with different rail pads kR = 300, 1000 kN/mm, compliances of the track

a) without and b) with vehicle-track interaction

b)

a)

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Figure 15-2: Tracks with different rail pads kR = 300, 1000 kN/mm, mobilities of the soil at

a) 4, b) 8 m distance from the track, including vehicle-track interaction

b)

a)

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Figure 15-3: Tracks with different rail pads kR = 300, 1000 kN/mm, mobilities of the soil at

a) 16, and b) 32 m distance from the track, including vehicle-track interaction

b)

a)

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Figure 15-4: Tracks with different slab material EP = 0.48, 1, 4, 10, 30 109 N/m

2,


b)

a)

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2,


interaction

b)

a)

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Figure 15-7: Slab tracks with different sleeper material ES = 1.5, 3, 6 1010

N/m2,


b)

a)

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N/m2, mobilities

of the soil at a) 4, b) 8 m distance from the track, including vehicle-track interaction

b)

a)

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N/m2, mobilities

of the soil at a) 16, and b) 32 m distance from the track, including vehicle-track interaction

b)

a)

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Figure 15-10: Slab tracks with different sleeper distances d = 0.6, 0.65 m, compliances of

the track a) without and b) with vehicle-track interaction

b)

a)

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Figure 15-11: Slab tracks with different sleeper distances d = 0.6, 0.65 m, mobilities of the

soil at a) 4, and b) 8 m distance from the track, including vehicle-track interaction

b)

a)

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Figure 15-12: Slab tracks with different sleeper distances d = 0.6, 0.65 m, mobilities of the

soil at a) 16, and b) 32 m distance from the track, including vehicle-track interaction

b)

a)

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16. APPENDIX F – THE GETRAC SYSTEM WITHOUT

AND WITH UNDER SLEEPER PADS

a)

b)

Figure 16-1: The GETRAC System a) without and b) with under sleeper pads

results of the parameter studies and prioritization for ... scp0-ga-2010-265754 rivas_bam_...

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